## Introduction to Comparative Statics

### The Simple Keynesian Model of Income Determination

Let ) denote the value of the aggregate supply of goods and services in the economy. Since this accrues as sales revenue to firms who then pay it out as incomes to suppliers of inputs, including labor, we also refer to Y as national income. The aggregate demand for goods and services has two components: consumption demand C and investment demand I. We take / as exogenous, but C is determined by Ihe consumption Junction c = < y, o < c < i where the constant c is the marginal propensity to consume. The equilibrium condition is that aggregate supply must equal aggregate demand, or

implying that when we substitute cl' for C and solve for Y.

This is illustrated in figure 1^-. 1, Along the horizontal axis we measure }', along the vertical. C, I. and aggregate demand C + I. Thus the 45 .ine O E shows the set of points at which C + / = V. that is, the set of possible equilibrium points. The line OC, with slope c, denotes the consumption function C = cY. and the horizontal line gives the exogenous investment level I. The line fC. also with slope c, is therefore the aggregate-demand function C + / = cY + /, and the point al which this intersects the 45 line gives the equilibrium income level Y' at which aggregate demand is equal to aggregate supply.

Figure 14.1 Equilibrium in the simple Keynesian model

The comparative-statics question we ask in this model is: How does a change in exogenous investment I affect the equilibrium income level f'*7

Algebraically, the answei is found simply by regarding Y" as a function of /, either implicitly, through the equilibrium condition c; i c + /

Figure 14.1 Equilibrium in the simple Keynesian model

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